How long does it take to get 5.1.1 OTA?

AT&T released 5.1.1 a couple of weeks ago, and I still haven't gotten a notification on my phone that the OTA update is ready to be installed. I check manually every day, too, but every time it says that the "update was interrupted" and I have to wait 24 hours. Is that because the server is busy and I'll just have to wait patiently as the update is being rolled out to AT&T phones over the air? (Yes, I know I can simply move the date forward one day and try again manually, but I don't want to inadvertently mess up the automatic OTA checks.)
I would really like to install 5.1.1 on my S6. Is there a way to speed things up? Is there an official AT&T image I can install through Kies or some other way?

Thanks!
--Ron